1. Field of the Invention
The present invention relates to communication systems and, more specifically, to devices for estimating parameters to facilitate the demodulation of the signals including chaotic waveforms.
2. Description of the Prior Art
Recent advances in the understanding of nonlinear circuits have shown that chaotic oscillators can synchronize or become entrained. This result appears to contradict the definition of chaos: complex, unpredictable dynamics of a deterministic system characterized most commonly as extreme sensitivity to initial conditions. However, if certain mathematical requirements are met, then a chaotic circuit (called the driving system) can be designed to drive a similar system (the receiving circuit or subsystem) and obtain a correlated response.
Several existing systems employ chaotic synchronization to achieve secure communications by using the chaotic signal to mask the secure information. In one approach, a chaotic signal is added to the communications channel, thereby hiding the information signal. At the receiver, a synchronous subsystem is used to identify the chaotic part of the signal, and the chaotic part is then removed to reveal the information signal. Presumably, the security in this approach is due to the difficulty in identifying and removing the chaotic signal from the noise.
A second approach uses a shift-key approach, in which an information signal is encoded using a different chaotic attractor for each symbol to be transmitted. The resulting waveform is a sequence of chaotic bursts, each generated by an attractor corresponding to a symbol of the discrete information signal. Upon reception, separate receiver subsystems, one for each possible symbol, are used to identify the bursts by detecting which of the multiple receiver subsystems has synchronized. This approach is limited to digital modulation and requires a more complex receiver than the present approach.
In one application, communication is achieved by detecting parameter mismatch between the transmitter and the receiver by looking at the power contained in the difference between the received signal and a replica generated using cascaded synchronous subsystems. These schemes recognize that this error signal is proportional to the mismatch, which is present due to parameter modulation at the transmitter, thereby providing a crude method for demodulation. This approach allows for analog modulation and demodulation; however, it will suffer when noise is present in the system.
An inverse system approach for decoding the modulation of a chaotic waveform effectively demodulates the signal by algebraically inverting part of the circuit. Other forms of communications using chaotic waveforms have been postulated in the literature, including techniques called phase space location modulation and chaotic digital encoding.
No device or method exists which estimates a modulation parameter in real time to emodulate a signal, such as a chaotic signal.